An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.40, and does not touch the bed. a. Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass. Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other.

Video transcript

Welcome back, everyone. We are given this system that is used for traction and we are tasked with finding what is the tension force inside of this system considering that the pulleys are frictionless here. Well, here's what we can do. Let me first draw a free body diagram of our mass down here. So we have that our mass, which I will represent with this point has two forces acting on it as follows. One, you're gonna have the tension force and then on the bottom, you're going to have the force due to gravity here. Now, what I'm gonna do is I'm actually going to denote the positive Y direction as our moving up or in the same direction as our tension force here. What we're gonna do is we're gonna use Newton's second law to figure out our tension force. We have that the sum of all forces in the Y direction is equal to mass times acceleration. What this translates to is T minus M G is equal to well zero because the mass is counterbalancing the leg and therefore not moving. This means that our tension is going to be equal to our mass times our gravity, which we can simply plug in our numbers that we are given. So let's go ahead and do that have that the mass of the block is five kg times our acceleration due to gravity, which is 9.8, which gives us a final answer of 49 newtons corresponding to our final answer. Choice of c Thank you all so much for watching. Hope this is for your help. We will see you all in the next one.